The orientifold Temperley--Lieb algebra
Representation Theory
2026-01-08 v1 Mathematical Physics
Combinatorics
math.MP
Quantum Algebra
Abstract
We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot's orientifold quiver Hecke algebras. We prove that the symplectic blob algebras are graded cellular and provide a conjectural algorithm for calculating their graded decomposition matrices. In doing so, we give the first explicit family of finite-dimensional graded quotients of the orientifold quiver Hecke algebras, providing a new entry point for the structure of these algebras -- in the spirit of Libedinsky--Plaza's ``blob algebra approach'' to modular representation theory.
Cite
@article{arxiv.2601.04012,
title = {The orientifold Temperley--Lieb algebra},
author = {Chris Bowman and Zajj Daugherty and Maud De Visscher and Rob Muth and Loic Poulain D'andecy},
journal= {arXiv preprint arXiv:2601.04012},
year = {2026}
}